If anything, people are undersharing—and that poses a massive challenge to the Facebook CEO's vision of Graph Search.

Zuckerberg unveiled Graph Search, a considerable upgrade to Facebook's notoriously weak search feature, last week, to much fanfare. For the lucky few who get access to it—Facebook is rolling it out slowly—it will be far easier to learn which friends are available for dating, who might be a good recruit, and which restaurants friends frequent.

All that assumes, however, that people actually share that data with Facebook. Graph Search can only search what people share. And it's not clear most users actually share enough to make searches on Facebook interesting..

Facebook has been testing Graph Search internally. But Facebook employees are notoriously heavy users of the service. As early employee Kate Losse chronicled in "The Boy Kings," her memoir of her time at the social network, sharing is expected as part of Facebook's culture.

Location is another form of data that Facebook has tried to get users to share. But that's mostly been a flop. Facebook's standalone Places feature, more or less a Foursquare clone, was killed off in favor of a subtler inclusion of location information in status updates and photo posts. And it turns out that most Internet users—even savvy smartphone owners—aren't interested in checking in.

Facebook has made attempts to get people to provide better local data—for example, encouraging users to rate restaurants after they check in. But that assumes they've checked in at all.

What about work-related searches for recruiting—a category Facebook engineering manager Lars Rasmussen highlighted at the launch of Graph Search?

Pete Kazanjy, the CEO of TalentBin, a recruiting search engine which gathers information about prospective hires across multiple social networks and websites, has actually run the numbers.

TalentBin hasn't analyzed all of Facebook's users. Kazanjy describes its sample set as "heavily biased towards Silicon Valley types who have more of a proclivity to fill this stuff out." Even among that tech set, fully half had no job information at all on their profile.

The other half, on average, provided 120 characters worth of information about their work history. LinkedIn users, by contrast, had 1,800 characters of work information—15 times as much data.

"There's zero threat to LinkedIn from structured data in Facebook," Kazanjy concludes—because the data isn't there to search on.

So much for finding new hires through Graph Search.

Facebook's most recent attempt to accelerate the pace of sharing, a strategy it called "frictionless sharing," seems to have flopped.

A category of apps called "news readers," which more or less tricked users who clicked on a news story shared by friends to install an app that similarly reported their reading habits, drove users crazy. After specifically recommending the frictionless approach to developers, Facebook backtracked, saying that those features lead to "low quality user experiences."

Outside of limited categories, like music and fitness apps, frictionless sharing seems dead—and with it, the ever-increasing pace of information posting predicted by Zuckerberg's law.

So where does that leave Graph Search?

One theory people have—and until Graph Search is rolled out at scale, it's nothing but a theory—is that once Facebook users figure out that the information they post is easy for friends to find, they'll share more.

But that could just as well go the other way: The ease with which photos, check-ins, and likes can now be found might scare users into sharing less.